The purpose is to practice more with abstract data types and a little with recursion. This assignment is taken from Data Structures and Abstractions with Java, by Frank M. Carrano and Walter Savitch, Prentice-Hall, 2003.
The state includes a numerator and a denominator, both of which are integers; negative fractions are possible. Be sure to handle zero denominators. A fraction should always be stored in lowest terms. Improper fractions are allowed (numerator > denominator).
Operations must include
To put a fraction in lowest terms, you need to compute the greatest common denominator of two integers. There is the famous Euclid's algorithm to do so:
gcd(a,b): if (a mod b) = 0 then return b else return gcd(b, a mod b)Always store the denominator as a positive number.
The state contains an integer portion and a fractional portion. The fractional portion should be in lowest terms and have its numerator less than its denominator.
The operations should be analogous to those for the Fraction class.
Use the operations in Fraction whenever possible. For instance, to add two mixed numbers, convert them to fractions, add the fractions using the Fraction class add method, and then convert the result to mixed number form.
Watch out for problems with the sign. For instance, you don't want to print out -5 -1/2 (you should print either 5 1/2 or -5 1/2).
Due by 10:20 AM on Wednesday, Feb 18: